Transverse Vibrations of Mixed-Mode Cracked Nanobeams With Surface Effect

Abstract

Slant edge cracked effect considering the inherent relation between surface energy and mixed-mode crack propagations on the free transverse vibrations of nanobeams with surface effect is investigated. First, the slant edge cracked effect, which considers residual surface stress effect on the crack tip fields of a mode-I and mode-II surface edge crack, is developed and the corresponding stress intensity factors (SIFs) and local flexibility coefficients are derived. Moreover, a refined continuum model of slant cracked nanobeams is established by considering both slant edge cracked effect and surface effect. The effects of fracture angles, crack depth, surface elasticity, surface stress, and surface density on the local flexibility and free transverse vibration characteristics of cracked nanobeams are, respectively, analyzed. The results show that the flexibility coefficients distribute symmetrically about residual surface stress. Fracture angles have a profound influence on both the symmetries of the mode shapes and the natural frequencies of nanobeams, and the influence becomes more pronounced as crack depth ratios increase. Furthermore, the natural frequencies will first decrease and then increase with fracture angles when the slant edge cracked effect is considered. The results demonstrate that the inherent relation between surface energy and crack propagations should be considered for both the stress distributions at the crack tip and the dynamic behavior of cracked nanobeams.